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What is the length of the hypotenuse of a right angled triangle whose other two sides are of length 8 units and 15 units?

In fig $x=$ ${30}^{\circ }$ the value of $(6y–3x)$ is

(a) Find the value of angle which is supplementary to itself. [2 MARKS]
(b) Find the angle which is double of its supplement.

1. 7

Which of the following can be the value of A if the number 27A49 is divisible by 3.

What is the area(in ${cm}^2$) of this triangle?
___

The following figure shows a quadrilateral in which sides AB and DC are parallel. If $\angle A:\angle D=4:5,\angle B=(3x-15{)}^{o}and\angle C=(4x+20{)}^o$, find each angle of the quadrilateral ABCD.

If a + b = 5 and ab = 6; find $a^2+b^2$

Fill in the blanks to make the statements true.

The square root of $5.3\times 5.3$ is ___

Question 1 (b)\angle{F}
Which congruence criterion do you use in the following?

Given: RP = ZX, RQ = ZY, $\angle PRQ=\angle XZY$
So, $\Delta PQR\cong \Delta XY$

Question 81 (c)

Express each of the following in single exponential form.
$5^2\times 7^2$

The runs scored by 11 players in a cricket match are 12, 32, 43, 32, 12, 32, 12, 32, 36, 54,11. Find the mode of the runs scored by the players. [2 MARKS]

$Inanentranceexamtherewerefoursectionswith50markseach.MarkssecuredbySatyamineachsectionisshownbelow$$$\begin{array}{ccccc}Subject& Aptitude& GeneralMathematics& GeneralAwareness& English\\ Marks& \text{45}& \text{40}& \text{35}& \text{40}\end{array}$$

What is the percentage marks scored by him in each section?

If I add a 2 digit number and the number formed by swapping digits, the resultant number is surely divisible by ___

What is the profit percent acquired when the cost price is ₹ 200 and selling price is ₹ 350?

In how much time will a sum of Rs. 1600 amount to Rs. 1852.20 at $5\%$ per annum compound interest?

Divide Rs. 7000 among A, B and C such that A gets 50$\%$ of what B gets and B gets 50$\%$ of what B gets and B gets 50$\%$ of what C gets.

Tick the correct answer in each of the following:

The compound interest on Rs 10000 at $10\%$ per annum for 3 years, compounded annually. is

(a) Rs 1331 (b) Rs 3310 (c) Rs 3130 (d) Rs 13310

$Ifx+y=4andxy=2,\text{find the value of}{x}^2+y^2.$

Factorize each of the following algebraic expressions.

$3a(x-2y)-b(x-2y)$

Question 91

Solve the following question:

Using prime factorization, find which of the following are perfect squares.

a) 484
b) 11250
c) 841
d) 729

Question 85(i)

The pie chart given below shows the result of a survey carried out to find the modes of travel used by the children to go school. Study the pie chart and answer the questions that follow.

What is The most common mode of transport ?

Question 69

State whether the following statement is true or false:

Let x and y be natural numbers. If x divides y, then $x^3$ divides $y^3$

Dividing $(a+b{)}^2+(a-b{)}^2$ by $a^2+b^2$ gives:

What are the different ways in which a ratio can be represented? [1 MARK]

What is the remainder when $3x^2-7x+5$ is divided by $x-1$

Question 3(c)

Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation.

p - 5 = 5 (0, 10, 5, -5)

Factorise :

$3x^5-48x$

Which of the following number can be used as terminating or non termating number: 1.$\frac{1}{4}$ 2.$\frac{11}{15}$ 3.$\frac{38}{81}$

Question 180(i)

Simplify

${[{\left(\frac{1}{2}\right)}^2-{\left(\frac{1}{4}\right)}^3]}^{-1}\times 2^{-3}$

6 cows can graze a field in 28 days. How long would 14 cows take to graze the same field ?

By using the formula, find the amount and compound interest on:

Rs 6000 for 2 years at $9\%$ per annum compounded annually.

Find 10 rational numbers between $\frac{-3}{4}$ and $\frac{5}{6}$

Pipe A can fill an empty tank in 5 hours while pipe B can empty the full tank In 6 hours. If both are opened at the same time in the empty tank, how much time will they take to fill it up completely?

Question 101 (ii)

Here is a keyboard fo a harmonium.

What is the ratio of black keys to all keys on the given keyboard?

Fiind the coordinates of points A,B,C,D in the figure.

A dishonest shopkeeper professes to sell pulses at his cost price but uses a false weight of 950 for each kilogram. Find his gain percent.

Question 83 (vii)

Multiply the following:

7pqr, (p - q + r)

1. 250

The area of trapezium whose parallel sides are 57 cm and 39 cm and the distance between them is 28 cm is

Simplify and write in exponential form: $5^3\times 5^{-1}\times {25}^2$

The compound interest on Rs 50,000 at 4% per annum for 2 years compounded annually is
(a) Rs 4,000
(b) Rs 4,080
(c) Rs 4,280
(d) Rs 4,050

Which method of finding the mean would you not use if you have class intervals whose values are big but they are close to each other?

An aquarium is in the form of a cuboid whose external measures are $50cm\times 40cm\times 30cm$. The base, side faces and back face are to be covered with a colored paper. Find the area of the paper needed? [ 3 MARKS ]

Question 72

In the following question, state whether the statement is True (T) or False (F):

Common factor of $12a^2{b}^2+4a{b}^2-32$ is 4.